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When the data are autocorrelated, this has a direct effect on the theoretical variance of the sample mean, which is [9] [¯] = [+ = ()]. The variance of the sample mean can then be estimated by substituting an estimate of σ 2. One such estimate can be obtained from the equation for E[s 2] given
This algorithm can easily be adapted to compute the variance of a finite population: simply divide by n instead of n − 1 on the last line.. Because SumSq and (Sum×Sum)/n can be very similar numbers, cancellation can lead to the precision of the result to be much less than the inherent precision of the floating-point arithmetic used to perform the computation.
In the general case, the unbiased estimate of the covariance matrix provides an acceptable estimate when the data vectors in the observed data set are all complete: that is they contain no missing elements. One approach to estimating the covariance matrix is to treat the estimation of each variance or pairwise covariance separately, and to use ...
This pre-aggregated data set becomes the new sample data over which to draw samples with replacement. This method is similar to the Block Bootstrap, but the motivations and definitions of the blocks are very different. Under certain assumptions, the sample distribution should approximate the full bootstrapped scenario.
The trade-off of variance-structure misspecification and consistent regression coefficient estimates is loss of efficiency, yielding inflated Wald test p-values as a result of higher variance of standard errors than that of the most optimal. [6]
It is especially useful for bias and variance estimation. The jackknife pre-dates other common resampling methods such as the bootstrap . Given a sample of size n {\displaystyle n} , a jackknife estimator can be built by aggregating the parameter estimates from each subsample of size ( n − 1 ) {\displaystyle (n-1)} obtained by omitting one ...
In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguished. [1] For example, the sample mean is a commonly used estimator of the population mean. There are point and interval ...
The sum of squared deviations needed to calculate sample variance (before deciding whether to divide by n or n − 1) is most easily calculated as = From the two derived expectations above the expected value of this sum is